General constructive representations for continuous piecewise-linear functions

The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most n-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests.     

A compact f-f model of high-dimensional piecewise-linear function over a degenerate intersection

A novel f-f model is developed constructively which can express any n-dimensional piecewise linear (PWL) function by a superposition of basis functions if it is defined over an nth-order degenerate intersection formed by (n-1)th-order minimal degenerate intersections. We also propose the concrete functional forms of nth-order basis functions. Being the simplest type of the minimal degenerate intersection, the basis function is the most elementary "building block" of a PWL function defined in an arbitrary-dimensional space. In addition, the model constitutes a natural continuation to Julian's canonical formulation and can bridge the lattice PWL model and the well-established canonical representation.     

A new algorithm for simulation of power electronic systems usingpiecewise-linear device models

This paper describes a new algorithm for simulation of power electronic systems. Piecewise-linear (PWL) approximation is used to model nonlinear components, including switching devices, nonlinear reactive components, and nonlinear control circuitry. A representation of PWL elements is constructed such that a constant system matrix is obtained, regardless of the states of PWL elements. An efficient method for state determination is proposed, which is capable of resolving difficulties caused by discontinuous characteristics of PWL elements. The resulting simulation algorithm is quite general, requires no prior knowledge of the circuit operation, is void of convergence problems, and yields relatively short simulation times on desktop PC machines     

Piecewise linear system modeling based on a continuous thresholddecomposition

The continuous threshold decomposition is a segmentation operator used to split a signal into a set of multilevel components. This decomposition method can be used to represent continuous multivariate piecewise linear (PWL) functions and, therefore, can be employed to describe PWL systems defined over a rectangular lattice. The resulting filters are canonical and have a multichannel structure that can be exploited for the development of rapidly convergent algorithms. The optimum design of the class of PWL filters introduced in this paper can be postulated as a least squares problem whose variables separate into a linear and a nonlinear part. Based on this feature, parameter estimation algorithms are developed. First, a block data processing algorithm that combines linear least-squares with grid localization through recursive partitioning is introduced. Second, a time-adaptive method based on the combination of an RLS algorithm for coefficient updating and a signed gradient descent module for threshold adaptation is proposed and analyzed. A system identification problem for wave propagation through a nonlinear multilayer channel serves as a comparative example where the concepts introduced are tested against the linear, Volterra, and neural network alternatives     

Digital design of sigmoid approximator for artificial neuralnetworks

A digital design for piecewise-linear (PWL) approximation to the sigmoid function is presented. Circuit operation is based on a recursive algorithm that uses lattice operators max and min to approximating nonlinear functions. The resulting hardware is programmable, allowing for the control of the delay-time/approximation-accuracy rate     

Piecewise-linear approximation of nonlinear dynamical systems

The piecewise-linear (PWL) approximation technique developed by Julia/spl acute/n et al. in the past few years is applied to find approximate models of dynamical systems dependent on given numbers of state variables and parameters. Referring to some significant examples, i.e., topological normal forms, it is shown that a PWL dynamical system approximating a given smooth system can preserve its main features. In particular, if the approximation accuracy increases, the equivalence between approximating and approximated systems shifts from qualitative to quantitative. The validity of the proposed approach is eventually tested by use of a severe nonlinear example, i.e., the Rosenzweig-MacArthur system, which describes the population dynamics in a tritrophic food chain model.     

On optimal and near-optimal turbo decoding using generalized max operator

Motivated by a recently published robust geometric programming approximation, a generalized approach for approximating efficiently the max* operator is presented. Using this approach, the max* operator is approximated by means of a generic and yet very simple max operator, instead of using additional correction term as previous approximation methods require. Following that, several turbo decoding algorithms are obtained with optimal and near-optimal bit error rate (BER) performance depending on a single parameter, namely the number of piecewise linear (PWL) approximation terms. It turns out that the known Max-Log-MAP algorithm can be viewed as special case of this new generalized approach. Furthermore, the decoding complexity of the most popular previously published methods is estimated, for the first time, in a unified way by hardware synthesis results, showing the practical implementation advantages of the proposed approximations against these methods.     

Test‐Generation‐Based Fault Detection in Analog VLSI Circuits Using Neural Networks

In this paper, we propose a novel test methodology for the detection of catastrophic and parametric faults present in analog very large scale integration circuits. An automatic test pattern generation algorithm is proposed to generate piece‐wise linear (PWL) stimulus using wavelets and a genetic algorithm. The PWL stimulus generated by the test algorithm is used as a test stimulus to the circuit under test. Faults are injected to the circuit under test and the wavelet coefficients obtained from the output response of the circuit. These coefficients are used to train the neural network for fault detection. The proposed method is validated with two IEEE benchmark circuits, namely, an operational amplifier and a state variable filter. This method gives 100% fault coverage for both catastrophic and parametric faults in these circuits.     

A Stochastic Approximation Approach to the Power-Control Problem

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense     

基于空间特征的非线性电路神经网络诊断

本文提出线性模拟电路的单、双、三故障空间特征,采用分段线性模型（PWL）将非线性电路线性化,通过遗传算法求电路的容羞范围,用神经网络对非线性嘲络进行诊断。本文的方法大火减少了模拟计算量,同时,使神经网络的训练过程加快,训练误差减少,并大大提高了诊断的正确率。     

Adaptive region growing technique using polynomial functions for image approximation

This paper presents an approximation algorithm for two-dimensional signals (e.g., images) using polynomial functions. The proposed algorithm is based on an adaptive segmentation of the original signal into adjacent regions and on the approximation of the signal in each region by a two-dimensional polynomial function. The segmentation is obtained by an adaptive region growing technique which allows perfect adaptation between the chosen approximation and the inner structure of the signal. Results of this technique are presented in the context of image coding applications.     

Piecewise linear CAD model for avalanche photodetectors

A simple CAD model for avalanche photodetectors (APD) is developed. The model is based on a piecewise linear (PWL) approximation of the responsivity curve of the APD which may be obtained either from theoretical considerations or from terminal measurements. The model takes into account nonlinear effects in the design of APD optical receivers.     

Greed is good: algorithmic results for sparse approximation

This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho's basis pursuit (BP) paradigm can recover the optimal representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function is introduced to quantify the level of incoherence. This analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal. From there, it argues that OMP is an approximation algorithm for the sparse problem over a quasi-incoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms.     

Fast and Efficient Search for All DC Solutions of PWL Circuits by Means of Oversized Polyhedra

A fast and efficient method for finding all dc solutions of resistive piecewise linear (PWL) circuits is proposed. This method is based on the introduction of suitable polyhedra, denoted as oversized, surrounding a sequence of certain portions of PWL characteristics. Unlike the minimum-sized polyhedra introduced in the standard polyhedral method, these oversized polyhedra are characterized by simple polygons (for example, triangles) with a low number of vertices. The overall algorithm is so structured according to a sequence of binary trees, composed of nodes connected by oriented arcs, and it is based on a linear programming test characterized by low-dimension tableaux. The advantages of using polyhedra with a few number of vertices are double: There are minor numerical errors in tableau solutions, and the total CPU time decreases remarkably. Therefore, it is possible to deal with higher rank circuits in comparison with the standard polyhedral method.     

Efficient and fast iterative reweighted least-squares nonrecursivefilters

An efficient and fast technique for designing L_p approximation filters using the iterative reweighted least-squares (IRLS) algorithm is proposed. This technique introduces an extra frequency response which implicitly includes the weighting function such that the filter coefficients can be obtained with O(N²) complexity     

规范化分段线性化动态网络的改进节点法

本文提出将规范化分段线性化电阻网络所有元件都看成电源的新思路，推导出规范化分段线性化网络改进节点法的完整表达式和相应的算法，它使规范化分段线性化动态网络的计算更加普遍化。文中有算例。     

Transient Simulation of Lossy Interconnects Based on a Dispersive Hybrid Phase-Pole Macromodel

A transient simulator for interconnect structures that are modeled by lossy transmission lines is outlined in this paper. Since frequency-dependent RLGC parameters must be employed to correctly model skin effects and dielectric losses for high-performance interconnects, we first study the behaviors of various lossy interconnects that are characterized by frequency-dependent line parameters (FDLPs). We then developed a frequency-domain dispersive hybrid phase-pole macromodel (DHPPM) for such lines, which consists of a constant RLGC propagation function multiplied by a residue series. The basic idea is to first extract the dominant physical phenomenology by using a propagation function in the frequency domain that is modeled by frequency-independent line parameters (FILPs). A rational function approximation is then used to account for the remaining effects of FDLP lines. By using a partial fraction expansion and analytically evaluating the required inverse Fourier transform integrals, the time-domain DHPPM can be decomposed as a sum of canonical transient responses for lines with FILP for various excitations (e.g., trapezoidal and unit step). These canonical transient responses are then expressed analytically as closed-form expressions involving incomplete Lipshitz-Hankel integrals of the first kind and Bessel functions. The closed-form expressions for these canonical responses are validated by comparing with simulation results from commercial tools like HSPICE. The DHPPM simulator can simulate transient results for various input waveforms on both single and coupled interconnect structures. Comparisons between the DHPPM results and the results produced by commercial simulation tools like HSPICE and a numerical inverse fast Fourier transform show that the DHPPM results are very accurate.     

基于核典型相关分析的字符识别

介绍一种基于核典型相关分析(KCCA)的字符识别方法.首先选取核函数将低维数据映射到高维空间,再利用典型相关分析(CCA)的思想对数据进行降维,最后利用分类器对降维后的数据进行分类识别.通过对MINST手写数字字符库的实验结果表明,利用KCCA对特征数据进行降维后,能够在新的特征空间中寻找到较好的线性模型,即新特征能够被较好地分类识别.     

Performance Assessment of Band-Limited Limiting and Blanking Communication Systems

This paper presents a general formulation of piecewise linear (PWL) models of voltage transfer functions to characterize channel nonlinearities in satellite digital communication systems. This formulation provides a tractable approach to evaluate the performance of such systems with band-limited PWL limiters, channel blanking, and hardlimiters. The envelope characteristics of the PWL models are derived in terms of breakpoints and slopes of PWL segments. Intermodulation (IM) products, their statistical properties, and the resultant error probability performance of such BPSK systems, subject to CW interference, are numerically illustrated through these PWL models.     

Cancellation of nonlinear distortion based on integration of FCM clustering algorithm and adaptive-two-stage linear approximation

A hybrid system of the fuzzy c-means （FCM） clustering algorithm and adaptive-two-stage linear approximation was presented for nonlinear distortion cancellation of radio frequency （RF） power amplifier （PA）. This mechanism can effectively eliminate noise, adaptively model PA＇s instantaneous change, and efficiently correct nonlinear distortion. This article puts forward the FCM clustering algorithm for clustering received signals to eliminate white noise, and then uses the adaptive-two-stage linear approximation to fit the inverse function of the amplitude＇s and phase＇s nonlinear mapping during the training phase. Parameters of the linear function and similarity function are trained using the gradient-descent and minimum mean-square error criteria. The proposed approach＇s training results is directly employed to eliminate sampling signal＇s nonlinear distortion. This hybrid method is realized easier than the multi-segment linear approximation and could reduce the received signal＇s bit error rate （BER） more efficiently.